290 
MR. S. DUNKERLEY ON THE WHIRLING 
The elimination of A : B : 0 : D from these equations gives either A = 0, B = 0, 
C = 0, D = 0, or sin ml = 0, i.e., 
ml = 3 - 1416 . 
11. Experimental Results .—For a description of the manner in which the experi¬ 
ments were made, see § 3, p. 283. 
The following are the mean results—the jjercentage errors being considered 
positive or negative according as the observed is greater or less than the calculated 
speed. 
Number 
of 
experiment. 
Date. 
Conditions. 
Observed 
speed. 
Calculated 
speed. 
Percentage error being 
observed-calculated 
100X , , 
observed 
2 
1 
June 22, 1892 
Free span of 2' 8” 
„ 2' 6” 
1119 
1293 
1121 
1275 
- -2 
-f -4 
The experiments show that, in the simple case of a shaft resting on two bearings 
in which the conditions required by the theory can be very closely approximated to 
in practice, there is no appreciable difference between the observed and calculated 
speeds. 
Case III. 
12. Shaft supported on bearings I feet apart and overhanging to a 
LENGTH C ON ONE SIDE. 
Thus— 
Fig. 
5. 
- I -- c - 
i i ! 
Taking the origin at A, we have from B to A, 
y ■=■ k. cosh mx + B sinh mx + C cos mx D sin mx. 
and, from A to C, 
y — A' cosh mx -j- B' sinh mx + C' cos mx + D' sin mx 
(§ 8, p. 287, equation 7). 
